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Perfectly-Secure Synchronous MPC with Asynchronous Fallback Guarantees

28 January 2022
Ananya Appan
Anirudh Chandramouli
Ashish Choudhury
ArXiv (abs)PDFHTML
Abstract

Secure multi-party computation (MPC) is a fundamental problem in secure distributed computing. An MPC protocol allows a set of nnn mutually distrusting parties to carry out any joint computation of their private inputs, without disclosing any additional information about their inputs. MPC with information-theoretic security provides the strongest security guarantees and remains secure even against computationally unbounded adversaries. Perfectly-secure MPC protocols is a class of information-theoretically secure MPC protocols, which provides all the security guarantees in an error-free fashion. The focus of this work is perfectly-secure MPC. Known protocols are designed assuming either a synchronous or asynchronous communication network. It is well known that perfectly-secure synchronous MPC protocol is possible as long as adversary can corrupt any ts<n/3t_s < n/3ts​<n/3 parties. On the other hand, perfectly-secure asynchronous MPC protocol can tolerate up to ta<n/4t_a < n/4ta​<n/4 corrupt parties. A natural question is does there exist a single MPC protocol for the setting where the parties are not aware of the exact network type and which can tolerate up to ts<n/3t_s < n/3ts​<n/3 corruptions in a synchronous network and up to ta<n/4t_a < n/4ta​<n/4 corruptions in an asynchronous network. We design such a best-of-both-worlds perfectly-secure MPC protocol, provided 3ts+ta<n3t_s + t_a < n3ts​+ta​<n holds. For designing our protocol, we design two important building blocks, which are of independent interest. The first building block is a best-of-both-worlds Byzantine agreement (BA) protocol tolerating t<n/3t < n/3t<n/3 corruptions and which remains secure, both in a synchronous as well as asynchronous network. The second building block is a polynomial-based best-of-both-worlds verifiable secret-sharing (VSS) protocol, which can tolerate up to tst_sts​ and tat_ata​ corruptions in a synchronous and in an asynchronous network respectively.

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